Re: DDD simulated by HHH cannot possibly halt (Halting Problem) --- mindless robots

On 4/14/2025 7:46 AM, olcott wrote:

On 4/13/2025 9:12 PM, dbush wrote:

On 4/13/2025 10:09 PM, olcott wrote:

On 4/13/2025 6:51 PM, dbush wrote:

On 4/13/2025 7:32 PM, olcott wrote:

On 4/13/2025 4:03 PM, dbush wrote:

On 4/13/2025 5:00 PM, olcott wrote:

On 4/13/2025 3:00 PM, dbush wrote:

On 4/13/2025 3:59 PM, olcott wrote:

On 4/13/2025 3:54 AM, joes wrote:

Am Fri, 11 Apr 2025 10:56:32 -0500 schrieb olcott:

On 4/11/2025 3:24 AM, Richard Heathfield wrote:

On 11/04/2025 08:57, Mikko wrote:

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No proof of this principle has been shown so its use is not valid.

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No proof of Peano's axioms or Euclid's fifth postulate has been shown.
That doesn't mean we can't use them.
Mr Olcott can have his principle if he likes, but only by EITHER
proving it (which, as you say, he has not yet done) OR by taking it as
axiomatic, leaving the world of mainstream computer science behind him,
constructing his own computational 'geometry' so to speak, and
abandoning any claim to having overturned the Halting Problem. Navel
contemplation beckons.
Axioms are all very well, and he's free to invent as many as he wishes,
but nobody else is obliged to accept them.
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*Simulating termination analyzer Principle*
It is always correct for any simulating termination analyzer to stop
simulating and reject any input that would otherwise prevent its own
termination.

Sure. Why doesn’t the STA simulate itself rejecting its input?
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Because that is a STUPID idea and categorically impossible
because the outermost HHH sees its needs to stop simulating
before any inner HHH can possibly see this.
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In other words, you agree that Linz and others are correct that no H exists that satisfies these requirements:
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Given any algorithm (i.e. a fixed immutable sequence of instructions) X described as <X> with input Y:
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A solution to the halting problem is an algorithm H that computes the following mapping:
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(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed directly
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No stupid! Those freaking requirements are wrong

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In other words, you have no interest in something that would make all truth provable.
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It will remain forever impossible to prove that five minutes
ago ever existed. This is empirical truth mislabeled as synthetic truth.
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Semantic truth poorly labeled as analytic truth is the only
truth that is either provable else untrue. It is {provable}
on the basis of semantic connections to expressions that are
stipulated as true.
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So you do want something that would make all truth provable.  An H that meets the following requirements would do that, therefore these requirements are not "wrong":
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*Ignorance on your part about this*
https://philosophy.stackexchange.com/questions/43748/how-do-we-know- the--wasnt-created-5-minutes-ago#:~:text=Ask%20Question,non- falsifiable%20and%20all).

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None-the-less an H that meets the requirements below would make all formal systems complete.  That makes such an H *very* useful, and therefore the requirements are not "wrong".
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Given any algorithm (i.e. a fixed immutable sequence of instructions) X described as <X> with input Y:
>
A solution to the halting problem is an algorithm H that computes the following mapping:
>
(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed directly
>
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 Such an HHH works fine when the input DD is not attempting
to do the opposite of whatever this HHH reports. This is not
a problem though. DD merely changes its own behavior through
the pathological self-reference that it implements.

Category error. DD is an algorithm, i.e. a fixed immutable sequence of instructions, therefore "changing its behavior" is impossible.  It only does exactly what its instructions say.

 Then HHH simply reports on this changed behavior. HHH need not
even know that DD is calling itself. It only need to know that
the behavior of DD would prevent its own termination.
 

In other words, HHH is changing the input and reporting on the changed input.
Changing the input is not allowed.